Proove that root 2 is irrational
Answers
Answered by
0
Answer:
ANSWER
Let us assume on the contrary that root2 is a rational number. Then, there exist positive integers a and bsuch that
root2=ba where, a and b, are co-prime i.e. their HCFis 1
⇒(root2)2=(ba)2
⇒2=b2a2
⇒2b2=a2
⇒2∣a2[∵2∣2b2 and 2b2=a2]
⇒2∣a...(i)
⇒a=2c for some integer c
⇒a2=4c2
⇒2b2=4c2[∵2b2=a2]
⇒b2=2c2
⇒2∣b2
Similar questions